Download or read book Constructions with Functions of Bounded Mean Oscillation written by Peter Wilcox Jones and published by . This book was released on 1978 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mean Oscillations and Equimeasurable Rearrangements of Functions written by Anatolii A. Korenovskii and published by Springer Science & Business Media. This book was released on 2007-09-19 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume considers various applications of equimeasurable function rearrangements to the "best constant"-type problems. It presents several classical theorems along with some very recent results. Coverage includes a product-space extension of the Rising Sun lemma, a product-space version of the John-Nirenberg inequality for bounded mean oscillation functions with sharp exponent, and sharp embedding theorems for Muckenhoupt, Gurov-Reshetnyak, and Gehring classes.
Download or read book Brownian Motion Hardy Spaces and Bounded Mean Oscillation written by Karl Endel Petersen and published by Cambridge University Press. This book was released on 1977-05-19 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exposition of research on the martingale and analytic inequalities associated with Hardy spaces and functions of bounded mean oscillation (BMO) introduces the subject by concentrating on the connection between the probabilistic and analytic approaches. Short surveys of classical results on the maximal, square and Littlewood-Paley functions and the theory of Brownian motion introduce a detailed discussion of the Burkholder-Gundy-Silverstein characterization of HP in terms of maximal functions. The book examines the basis of the abstract martingale definitions of HP and BMO, makes generally available for the first time work of Gundy et al. on characterizations of BMO, and includes a probabilistic proof of the Fefferman-Stein Theorem on the duality of H11 and BMO.
Download or read book Bounded Mean Oscillation in Complex Analysis written by Ilpo Laine and published by . This book was released on 1989 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On BMO Bounded mean Oscillation and related spaces written by Svante Janson and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Brownian Motion Hardy Spaces and Bounded Mean Oscillation written by and published by . This book was released on 1977 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mean Oscillations and Equimeasurable Rearrangements of Functions written by Anatolii A. Korenovskii and published by Springer Science & Business Media. This book was released on 2007-09-12 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume considers various applications of equimeasurable function rearrangements to the "best constant"-type problems. It presents several classical theorems along with some very recent results. Coverage includes a product-space extension of the Rising Sun lemma, a product-space version of the John-Nirenberg inequality for bounded mean oscillation functions with sharp exponent, and sharp embedding theorems for Muckenhoupt, Gurov-Reshetnyak, and Gehring classes.
Download or read book Geometric Inequalities and Bounded Mean Oscillation written by Ryan Gibara and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study the space of functions of bounded mean oscillation (BMO) on shapes. We prove the boundedness of important nonlinear operators, such as maximal functions and rearrangements, on this space and analyse how the bounds are affected by the underlying geometry of the shapes. We provide a general definition of BMO on a domain in R^n, where mean oscillation is taken with respect to a basis of shapes, i.e. a collection of open sets covering the domain. We prove many properties inherent to BMO that are valid for any choice of basis; in particular, BMO is shown to be complete. Many shapewise inequalities, which hold for every shape in a given basis, are proven with sharp constants. Moreover, a sharp norm inequality, which holds for the BMO norm that involves taking a supremum over all shapes in a given basis, is obtained for the truncation of a BMO function. When the shapes exhibit some product structure, a product decomposition is obtained for BMO. We consider the boundedness of maximal functions on BMO on shapes in R^n. We prove that for bases of shapes with an engulfing property, the corresponding maximal function is bounded from BMO to BLO, the collection of functions of bounded lower oscillation. When the basis of shapes does not possess an engulfing property but exhibits a product structure with respect to lower-dimensional shapes coming from bases that do possess an engulfing property, we show that the corresponding maximal function is bounded from BMO to a space we define and call rectangular BLO. We obtain boundedness and continuity results for rearrangements on BMO. This allows for an improvement of the known bound for the basis of cubes. We show, by example, that the decreasing rearrangement is not continuous on BMO, but that it is both bounded and continuous on VMO, the subspace of functions of vanishing mean oscillation. Boundedness for the symmetric decreasing rearrangement is then established for the basis of balls in R^n.
Download or read book Bounded Mean Oscillation BMO written by and published by . This book was released on 1978 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Functions of Bounded Mean Oscillation Characterized by a Restricted Set of Martingale Or Riesz Transforms written by Michael Frazier and published by . This book was released on 1983 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bounded Analytic Functions written by and published by Academic Press. This book was released on 1981-10-12 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bounded Analytic Functions
Download or read book Double Index Square Functions and Bounded Mean Oscillation on the Bidisc written by Jill Catherine Pipher and published by . This book was released on 1985 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Holomorphic Functions of Bounded Mean Oscillation written by Chong Mun Ho and published by . This book was released on 1995 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bounded Analytic Functions written by John Garnett and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The last seven of the ten chapters are devoted in the main to these recent developments. The motif of the theory of Hardy spaces is the interplay between real, complex, and abstract analysis. While paying proper attention to each of the three aspects, the author has underscored the effectiveness of the methods coming from real analysis, many of them developed as part of a program to extend the theory to Euclidean spaces, where the complex methods are not available.
Download or read book Vector Measures of Bounded Mean Oscillation written by O. Blasco de la Cruz and published by . This book was released on 1985 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Fourier Analysis written by Loukas Grafakos and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The great response to the publication of the book Classical and Modern Fourier Analysishasbeenverygratifying.IamdelightedthatSpringerhasofferedtopublish the second edition of this book in two volumes: Classical Fourier Analysis, 2nd Edition, and Modern Fourier Analysis, 2nd Edition. These volumes are mainly addressed to graduate students who wish to study Fourier analysis. This second volume is intended to serve as a text for a seco- semester course in the subject. It is designed to be a continuation of the rst v- ume. Chapters 1–5 in the rst volume contain Lebesgue spaces, Lorentz spaces and interpolation, maximal functions, Fourier transforms and distributions, an introd- tion to Fourier analysis on the n-torus, singular integrals of convolution type, and Littlewood–Paley theory. Armed with the knowledgeof this material, in this volume,the reader encounters more advanced topics in Fourier analysis whose development has led to important theorems. These theorems are proved in great detail and their proofs are organized to present the ow of ideas. The exercises at the end of each section enrich the material of the corresponding section and provide an opportunity to develop ad- tional intuition and deeper comprehension. The historical notes in each chapter are intended to provide an account of past research but also to suggest directions for further investigation. The auxiliary results referred to the appendix can be located in the rst volume.
Download or read book Continuous Exponential Martingales and BMO written by Norihiko Kazamaki and published by Springer. This book was released on 2006-11-15 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: In three chapters on Exponential Martingales, BMO-martingales, and Exponential of BMO, this book explains in detail the beautiful properties of continuous exponential martingales that play an essential role in various questions concerning the absolute continuity of probability laws of stochastic processes. The second and principal aim is to provide a full report on the exciting results on BMO in the theory of exponential martingales. The reader is assumed to be familiar with the general theory of continuous martingales.
